If you are typing text into the title of the note, then there is no return key because a title can only be one line. If you are typing text into the body of the note, then there should be a return key. I just checked both my iPhone and iPad and confirmed this. I think you may be typing into the title.
I had the same problem initially. Only applies to new release of iOS version. Caused by confusing labeling in the new iOS format: When you start a NEW note or go to a note that has only one line of text, the "body" field below the title only shows "tap to add note". Making it easy to assume that means "Tap to add NEW note or to finish editing this note" which you aren't wanting to do. If you tap there , you will now be editing the body of your note, and the return key will be available. If there is already text in the body, then it will be obvious.
Ahh, adjusting to new versions...
On the web version, you get a single form to complete, with the title and note content (and folder selector) being visible. This is intuitive and allows the user to add a note as a single action.
On IOS, the note title, content and folder selector are separated. This means that adding a new note in a certain folder requires 3 discrete actions from the user without an obvious workflow to guide you through. This is lot less intuitive (requiring knowledge from the user on how this works) and is inefficient (requires a lot of clicking about). It is easy to get lost on this user journey.